I can I shape a 3D object in a 2D, and the put the unwrap in a new 3D conformation without any deformations?
The answer is by no means without flaw. 

Start by enabling Import-Export UV Layout &amp;&amp; Import-Export: Scalable Vector Graphics in add-ons



In UV editor select desired map + open UVs menu --> Export UV Layout



Make sure to export as .svg



Last File --> Import --> svg



Every polygon is going to be its own curve so Alt + C --> convert to mesh from curve and join them after. 

It's not perfect